Cross Sectional Area Given Time Required To Lower Liquid Surface Using Bazins Formula Calculator

Bazins Formula:

\[ A_R = \frac{\Delta t \cdot m \cdot \sqrt{2 \cdot g}}{(\frac{1}{\sqrt{h_2}} - \frac{1}{\sqrt{H_{Upstream}}}) \cdot 2} \]

Time Interval (Δt):

Bazins Coefficient (m):

Acceleration due to Gravity (g):

m/s²

Head on Downstream of Weir (h₂):

Head on Upstream of Weir (H_Upstream):

Cross-Sectional Area of Reservoir (A_R):

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1. What is Bazins Formula?

Bazins Formula is used to calculate the cross-sectional area of a reservoir based on the time required to lower the liquid surface, incorporating factors such as Bazins coefficient, gravitational acceleration, and head measurements at upstream and downstream of a weir.

2. How Does the Calculator Work?

The calculator uses Bazins Formula:

\[ A_R = \frac{\Delta t \cdot m \cdot \sqrt{2 \cdot g}}{(\frac{1}{\sqrt{h_2}} - \frac{1}{\sqrt{H_{Upstream}}}) \cdot 2} \]

Where:

\( A_R \) — Cross-Sectional Area of Reservoir (m²)
\( \Delta t \) — Time Interval (s)
\( m \) — Bazins Coefficient
\( g \) — Acceleration due to Gravity (m/s²)
\( h_2 \) — Head on Downstream of Weir (m)
\( H_{Upstream} \) — Head on Upstream of Weir (m)

Explanation: The formula calculates the reservoir's cross-sectional area by considering the time interval for liquid surface lowering and the hydraulic characteristics at the weir.

3. Importance of Cross-Sectional Area Calculation

Details: Accurate calculation of cross-sectional area is crucial for reservoir design, capacity planning, flood control, and hydraulic engineering applications.

4. Using the Calculator

Tips: Enter time interval in seconds, Bazins coefficient, gravitational acceleration in m/s², and head measurements in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is Bazins Coefficient?
A: Bazins Coefficient is an empirical constant that accounts for the characteristics of the weir and flow conditions.

Q2: Why is gravitational acceleration included?
A: Gravitational acceleration affects the flow velocity and thus the time required for the liquid surface to lower.

Q3: What are typical values for Bazins Coefficient?
A: Bazins Coefficient typically ranges between 0.4-0.5, but exact values depend on specific weir geometry and flow conditions.

Q4: When is this formula most applicable?
A: This formula is particularly useful for rectangular weirs and reservoirs with relatively constant cross-sectional areas.

Q5: What are the limitations of Bazins Formula?
A: The formula assumes ideal flow conditions and may require adjustments for complex geometries or turbulent flow conditions.